Robust support vector regression with generic quadratic nonconvex ε-insensitive loss

Abstract

In this paper, we propose a robust support vector regression with a novel generic nonconvex quadratic ε-insensitive loss function. The proposed method is robust to outliers or noise since it can adaptively control the loss value and decrease the negative influence of outliers or noise on the decision function by adjusting the elastic interval parameter and adaptive robustification parameter. Given the nature of the nonconvexity of the optimization problem, a concave-convex programming procedure is employed to solve the proposed problem. Experimental results on two artificial data sets and three real-world data sets indicate that the proposed method outperforms support vector regression, L1-norm support vector regression, least squares support vector regression, robust least squares support vector regression, and support vector regression with the Huber loss function on both robustness and generalization ability.